Fractal Cold Gas as Dark Matter in Galaxies and Clusters

The conjecture that dark matter in galaxies is mostly cold fractal gas is developed in the more general context of the thermodynamics of the ideal isothermal gas subject to gravitational instability. This simple gas model already contains the contrary ingredients able to prevent an asymptotic equilibrium: any growing gravothermal singularity evaporates in a finite time, and any tendency to uniform gas is gravitationally unstable. The paradox is simply resolved by allowing fractal states, which are then scale-free and steady {\it in average}, but non-differentiable and time-dependent. If we apply to clusters the lessons learned with galaxies, we are led to the conclusion that gas in clusters at a temperature much below the virial temperature should also adopt a fractal structure and become inhomogeneous. The same instrumental biases acting at galactic scale and preventing the detection of the smallest and coldest sub-resolution clumps in the fractal are then even more relevant for cluster gas measurements. The large baryonic mass observed in the cluster hot gas and the morphology-density relation suggest also gaseous dark matter in spirals. If this dark gas component remains undetected in spirals, the same instrumental biases should hold in clusters, where cooling hot gas disappears from detection near the centre.